A Discrete Version of the Half-Logistic Distribution Based on the Mimicking of the Probability Density Function

We introduce a count distribution obtained as a discrete analogue of the continuous half-logistic distribution. It is derived by assigning to each non-negative integer value a probability proportional to the corresponding value of the density function of the parent model. The main features of this new distribution, in particular related to its shape, moments, and reliability properties, are described. Parameter estimation, which can be carried out resorting to different methods including maximum likelihood, is discussed, and a numerical comparison of their performances, based on Monte Carlo simulations, is presented. The applicability of the proposed distribution is proved on two real datasets, which have been already fitted by other well-established count distributions. In order to increase the flexibility of this counting model, a generalization is finally suggested, which is obtained by adding a shape parameter to the continuous one-parameter half-logistic and then applying the same discretization technique, based on the mimicking of the density function.